Integrability of invariant metrics on the Virasoro group
Each right-invariant metric on the Virasoro group induces a Hamiltonian vector field on the dual of the Lie algebra Dir equipped with the canonical Lie-Poisson structure. We show that the Hamiltonian vector fields X-k induced by the metrics given at the identity by the H-k Sobolev inner products, k >= 0, are bi-Hamiltonian relative to a modified Lie-Poisson structure only for k = 0 and k = 1. (c)